16w^2-12=48

Solution for 16w^2-12=48 equation:

16w^2-12=48

We move all terms to the left:

16w^2-12-(48)=0

We add all the numbers together, and all the variables

16w^2-60=0

a = 16; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·16·(-60)
Δ = 3840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*16}=\frac{0-16\sqrt{15}}{32}
=-\frac{16\sqrt{15}}{32}
=-\frac{\sqrt{15}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*16}=\frac{0+16\sqrt{15}}{32}
=\frac{16\sqrt{15}}{32}
=\frac{\sqrt{15}}{2}
$